Are you suggesting that a 'neutral accent' is only applicable to British English? What about Americans or other nationalities who also claim neutrality? Also, do you differentiate between Queens and RP? Because claiming that RP (generally the variety spoken by BBC news broadcasters) is without regional influence is a fallacy.

Regional accents and dialects, both. Americans do not have a neutral accent, it’s American English, very different to that of British English in both accent and dialect. Within British accents there are also many variations; if you’ve ever heard a Scottish or ‘Geordie’ (N.E. accent), you’ll know it’s not neutral and not easily understood by others.
The Queens English as formal speech is understood by all because it contains no regional or country accent or dialect and is the type of accent often referred to by recruiters as ‘neutral’.
The Queens English doesn’t have an accent and so isn’t regional, unlike Cockney, Liverpudlian, Mancunian . . . It’s why it’s called Queens English.

I think the view that neutral accent = RP/Queens English/BBC English is narrow-minded.
Certainly a neutral accent is one that is not regionally bound, and therefore is more likely to be understood by all. RP is generally agreed to fit that description. But is it the only neutral accent? I would disagree.
Some people claim that General American is an American equivalent of RP, though others dispute this. The US does have different accents, though I can only spot notable differences between a New Yorker and a Texan! This is mainly due to my ignorance of US accents.
RP as English's neutral accent may be a dated idea with so much variety of English around the world, surely it's possible other non-regionally bound English accents could be identified among higher level language learners. And these would potentially be neutral in an even greater sense in that they would transcend race, culture and class.
You allude to this same conclusion, John, calling Queens English "the type of accent", and therefore not the only neutral accent.
But ultimately neutral accent seems to be used most often as a term without a precise meaning. If a student is told to aim for a neutral accent, it means to try and minimise their native accent because it is interfering with understanding. If an employer asks for someone to have it, they want to know they don't have a strong regional accent, and may even accept a candidate with a mild regional accent, providing they are generally understood.

I really don't believe there is such a thing as a neutral accent. I've been many places and listened to plenty of people and conversations. Everyone I've encountered has a distinct sound in their voice. Some are more familiar to me and my heritage but that does not mean that it would be neutral to others coming from a different geographical location.

If a "neutral" accent is the one most people understand, then a "neutral" accent is British, since most of the English speakers in the world were taught by British (or British taught) teachers. Neutral Accent: An Accent The World Understands Neutral accent is a way of speaking a language without regionalism. Speaking with an accent affects our communication and sometimes at its worst spoils our image in public. To make ourselves understand better we should speak in neutral accent.

Almost invariably, recruiters in the East will request a skype interview in which they’re looking for personal presentation and accent. The way to disguise an accent is to speak slowly and clearly (pronunciation and enunciation) to disguise it. If a foreign interviewer is able to clearly understand, any accent variation will most likely be forgiven.

If I took a survey of all my students in China, they all want to sound like they grew up in Southern California. So if there is to be a 'neutral' English, maybe the customer should decide. They do decide with their dollar, not the pound. ;-)

The best English accent for your SS from China is Chinese, whether they pay in dollars, pounds or renminbi. The goal of some artificially neutral or even “perfect” accent is absurd, not to mention fake

"We are not wholly bad or good, who live our lives under Milk Wood " — Dylan Thomas, Under Milk Wood